Search This Blog


Tuesday, January 14, 2014

DO Events Cause Rapid Warming Events in the Last Glacial Period

Here is my evidence that DO [Dansgaard-Oeschger] events are
associated with rapid warming periods in the glacial record.

The the top figure in the graph below uses the GRIP chronology
from 0 to 45,000 BP.

There is some controversy about the GISP2, GRIP and NGRIP
scaling chronologies for the Greenland ice core. Shown below
are the timing of DO events 0, 2, 8, 11, 12, and 13 using the latest
NGRIP-based Greenland Ice Core Chronology 2005 (GICC05)
time scale to the period between 14.9 – 32.45 ka b2k (before
A.D. 2000) [Thanks to Rodger Andrews for pointing this out].


Note that DO events 0, 2, 8, 11, 12, and 13 have been placed
on this new scale.

Wednesday, January 8, 2014

The Long-Term Periodicities of the VEJ Spin-Orbit Coupling Model

The reader should be familiar with the contents of the
following paper before continuing with this post:

Wilson I.R.G., The Venus–Earth–Jupiter spin–orbit 
coupling model, Pattern Recogn. Phys., 1, 147–158,

which can be freely downloaded at:

In this paper, Wilson (2013) constructs a Venus–Earth
–Jupiter spin–orbit coupling model from a combination
of the Venus–Earth–Jupiter tidal-torquing model and
the gear effect. The new model produces net tangential
torques that act upon the outer convective layers of the
Sun with periodicities that match many of the long-term
cycles that are found in the 10Be and 14C proxy records
of solar activity.

Wilson (2013) showed that there are at least two 
ways that the Jovian and Terrestrial planets can 
influence bulk motions in the convective layers 
of the Sun. 

The first is via the VEJ tidal-torquing process:

– Tidal bulges are formed at the base of the convective
layers of the Sun by the periodical alignments of Venus
and the Earth.

– Jupiter applies a tangential gravitational torque to these
tidal bulges that either speed-up or slow-down parts of
the convective layer of the Sun.

– Jupiter’s net tangential torque increases the rotation rate
of the convective layers of the Sun for 11.07 yr (seven
Venus–Earth alignments lasting 11.19 yr) and then
decreases the rotation rate over the next 11.07 yr.

– The model produces periodic changes in rotation rate
of the convective layers of the Sun that result a 22.14 yr
(Hale-like) modulation of the solar activity cycle ( 14
Venus–Earth alignments lasting 22.38 yr).

– There is a long-term modulation of the net torque that
is equal to the mean time required for the 11.8622 yr
periodic change in Jupiter’s distance from the Sun to
realign with the 11.0683 yr tidal-torquing cycle of the
VEJ model.

The second way is via modulation of the VEJ 
tidal-torquing process via the gear effect:

The gear effect modulates the changes in rotation rate of
the outer convective layers of the Sun that are being
driven by the VEJ tidal-torquing effect.

– This modulation is greatest whenever Saturn is in
quadrature with Jupiter. These periodic changes in the
modulation of the rotation rate vary over a 19.859 yr

– The gear effect is most effective at the times when Venus
and the Earth are aligned on the same side of the Sun.

– There is a long-term modulation of the net torque that
has a period of 192.98 yr.

Note: The sidereal orbital periods used in this post are
those provided by:

 = sidereal orbital period of Venus = 0.615187(1) yrs

= sidereal orbital period of the Earth = 1.000000 yrs

= sidereal orbital period of Jupiter = 11.8617755(6) yrs

= sidereal orbital period of Saturn = 29.45663 yrs

= synodic period of Venus/Earth = 1.59866(5) yrs

= synodic period Jupiter/Saturn = 19.8585(3) yrs

The Physical Meaning for each of the Periodicities

The 22.136 Year Period of the VEJ Tidal-Torquing Model 

This is the time over which the angle between the nearest
VE tidal bulge (formed in the convective layers of the Sun)
and Jupiter moves from 0 to 180 degrees

Jupiter's net tangential torque increases the rotation rate of
the Sun's convective layers for the first 11.068 years and
then decreases the rotation rate for the remaining 11.068

Hence, the basic unit of change in the Sun’s rotation rate
(i.e. an increase followed by a decrease in rotation rate)
is 2 × 11.068 yr = 22.137 yr. This is essentially equal
to the mean length of the Hale magnetic sunspot cycle of
the Sun, which is 22.1 ± 2.0 yr (Wilson, 2011).

The 22.136 year period is simply half the realignment
time between Venus, the Earth and Jupiter (= 44.272
years) and it can be represented by the equation:

(Paul Vaughan - private communications).

The 165.42 year Modulation Period of the
Net Tangential Torque of Jupiter 

The 11.068 year period in the net tangential torque of
Jupiter acting upon the base of the Sun's convective
layer is modulated by the 11.862 year variation in the
mean distance of Jupiter from the Sun. This produces
a 165.42 year modulation in Jupiter's peak net tangential
torque given by:

The 193.02 year Modulation Period of the Gear Effect

The is the time required for the 22.137 yr periodicity of the
net tangential torque of Jupiter associated with the VEJ
Tidal-Torquing model to re-align with the 19.859 yr period
associated with the gear effect:

which can also be written as;

linking this modulation cycle to a multiple of the
period of time required for the planets Venus, the Earth,
Jupiter and Saturn to re-synchronize their orbits.

The 88 Year Gleissberg Cycle

The 88 year Gleissberg Cycle is a well identified
long-term periodicity that is seen in the level of solar
activity. The following equation shows that is merely
the synodic beat period between half the synodic
period of Jupiter/Saturn (= 9.9293 yrs) and seven
time the synodic period of Venus/Earth = 11.191 yrs.

Half the synodic period of Jupiter/Saturn is the time
between successive quadratures of Jupiter and Saturn
which is the main periodicity of the gear effect, while
seven times the synodic period of Venus/Earth
is the periodicity of the link between the VEJ
tidal-torquing model and the gear effect.

Of course, multiples of the Gleissberg period
correspond to long-term periodicities that were found
by McCracken et al. [2012]:

1 x 88.09 = 88.09 yrs --> 87.3 ± 0.4 yrs
4 x 88.09 = 352.36 yrs --> 350 ± 0.7 yrs
6 x 88.09 = 528.54 yrs --> 510 ± 15 yrs
8 x 88.09 = 704.72 yrs --> 708 ± 28 yrs

7 x 165.42 yrs = 6 x 193.02 yrs ≈ 1158 yrs

The following formula are direct consequence of
the above commensurablity:

The last equation links the orbital periods Venus and
the Earth to those of Jupiter and Saturn.

Sunday, December 15, 2013

Variations in the Earth's Climate on Decadal Time Scales and Proxigean Spring Tides

Richard Ray (2007) has made the bold claim that:

"Occasional extreme tides caused by unusually favorable
alignments of the moon and sun are unlikely to influence
decadal climate, since these tides are of short duration
and, in fact, are barely larger than the typical spring
tide near lunar perigee."

This post sets out to show that this claim is not completely true.

Richard Ray and David Cartwright (2007) have calculated
the strengths and dates of the maximal lunar-solar tidal potentials
over the period from 1 to 3000 A.D.  Thankfully, Prof. Ray has
kindly made this data available upon request. The following
arguments are based upon this data set which is known as the
Ray-Cartwright Table.

Figure 1 below shows the total equilibrium ocean tides (T)
caused by the lunar-solar tides between the years 2000
and 2010 A.D i.e.

T = (Vtot)/g

where Vtot is the total tidal potential due to the Sun and Moon,
g is the acceleration due to gravity (= 9.82 m/s/s) and T
is in cm.

Note: The terms "equilibrium ocean tide" and "tidal 
potential" are used interchangeably in this post, however, 
both refer to the equilibrium ocean tide heights measured 
in cm.

Figure 1

From figure 1 we can see that:

a) The total lunar-solar tidal potential (Vtot - green curve) is the
sum of the lunar tidal potential (Vlun - red curve) and the solar
tidal potential (Vsol - blue curve).

b) Vsol peaks once every year when the Earth is at or near
perihelion (blue curve).

c) The largest values of Vlun occur whenever the subtended angle
of the Sun and Moon (as seen from the Earth's centre) is either
less than 9 degrees (i.e. close to New Moon) or greater than
171 degrees (i.e. close to Full Moon). This means that the
largest values of Vlun occur very close to each New and Full
Moon where they produce the Spring Tides (red curve).

d) The largest values of Vlun peak roughly once every 206 days
when the spring tides occur at perigee. These tides are known
as Perigean Spring Tides. The 206 year period is associated
with the changing angle between the lunar line-of-apse and the
Earth-Sun direction. This angle is determined by the combined
motion of the Earth about the Sun and the precession of the
lunar line-of-apse. The lunar line-of-apse takes 411.78 days to
re-align with Earth-Sun line [note: 411.78/2 = 205.89 days].

e) Vtot (i.e. Vlun + Vsol - green curve) varies up and down
between 55 and 62 centimetres once every every 206 days.

Hence, first impressions indicate that Ray (2007) and Ray
and Cartwright (2007) correctly concluded that if you
compare peak Perigean spring tides with typical Perigean
spring tide that are adjacent in time, there is little or no
difference in their relative strength on decadal time scales
[e.g. compare  Perigean spring tides with total potentials
that are greater than 60 cm in figure 1].

However, Ray (2007) and Ray and Cartwright (2007) have
missed one important detail. The problem with their simple
analysis is that it does not take into account the different ways
in which the lunar tides can interact with the Earth’s climate

The most significant large-scale systematic variations upon the
Earth's climate on an inter-annual to decadal time scale, are
those caused by the annual seasons. These variations are
predominantly driven by changes in the level of solar insolation
with latitude that are produced by the effects of the Earth's
obliquity and its annual motion around the Sun.

This raises the possibility that the lunar tides act in "resonance"
with (i.e. subordinate to) the atmospheric changes caused by the
far more dominant solar driven seasonal cycles. With this type of
simple “resonance” model, it is not so much in what times do the
lunar tides reach their maximum strength, but whether or not
there are peaks in their strengths that re-occur at the same time
within the annual seasonal cycle.

A good analogy is a child on a swing. If you consider the annual
seasons as being the equivalent of the child on the swing as they
slowly move back and forward then the lunar tides can be
thought of as the hand of the person who pushes the swing.
Clearly, the hand pushing the swing is most effective in imparting
energy to the child on the swing if they give a push at the highest
point of their motion. Similarly, peak lunar tides should have their
greatest impact upon the seasonal swings of the climate system if
they are applied at a specific point in the seasonal cycle e.g. the
summer or winter solstices.

Figure 2 shows all of the total tidal potentials listed in the
Ray-Cartwright Table that occur in the month of January
between the years 1900 and 2010 A.D.

Figure 2

It is immediately evident from figure 2 that simply limiting the total
tidal potentials to those that affect the Earth's climate system in
January produces significant variations in the total tidal potential
on decadal time scales. Figure 2 shows that the peak equilibrium
ocean tide (or total tidal potential) varies by +/- 7 %  either side
of its mean peak value of 59 cm on a time scale of 4.425 years.

Note: The repetition cycle of 4.425 years is simply half the 
time required for the lunar line-of-apse to precess once 
around Earth with respect to the stars. 

Even greater decadal variations in the total tidal potential are
produced if we differentiate between those that occur at New
Moon in January (Figure 3) from those that occur at Full Moon
in January (Figure 4).

Figure 3

Figure 3 shows that the peak equilibrium ocean tide (or total tidal
potential) at New Moon vary by +/- 13.5 %  either side of their
mean peak value of 55.5 cm, on a time scale of 8.85 years.

Figure 4

While figure 4 shows that the peak equilibrium ocean tide (or
total tidal potential) at Full Moon vary bu the same amount over
the same time scale of 8.85 years. However, the peak tidal
potentials are shifted in phase by 180 degrees (equivalent to
4.425 years).

The effect of lunar phase on the magnitude of monthly
variation in the total tidal potential on decadal time scales
must be accounted for because at times near summer/winter
solstice i.e. during the months of December or January and
June or July, the tides induced by spring tides at New and
Full Moon affect distinctly different parts of the planet.

Figure 5 shows the latitude of the sub-lunar point on the
Earth's surface for each of the tidal potentials produced
by the (near) New and (near) Full Moons that are
displayed in figures 3 and 4.

Figure 5

We see that in figure 5 that the latitude of the sub-lunar points
of all of the New Moons on the Earth's surface are between
about 13 and 28 degrees South while the sub-lunar points
of all of the Full Moons on the Earth's surface are between
about 12 and 29 degrees North.

Note: Figure 5 shows that a clear 18.6 year sinusoidal 
variation in the latitude of the sub-lunar points tales 
place in each hemisphere. 

One way to correct the tidal potentials for the substantial
differences in latitude between New and Full Moon is to
multiply each potential by the cosine of the difference in
latitude between its sub-lunar point and 23.5 degrees South.
This give the approximate vertical tidal potential for each
New and Full Moon event at a latitude of 23.5 degrees
South (on the Earth's surface).

Figure 6

Figure 6 shows that the total equilibrium ocean tide corrected
to a latitude of 23.5 degrees South. We can see from this
figure that the tidal potentials at New Moon dominate total
tidal potential. This means that the peak total equilibrium ocean
tide (or peak total tidal potential) varies by +/- 13.5 %  either
side of its mean peak value of 55.5 cm, on a time scale of 8.85

Note: All the claims that are made in this post by the 
author also applies if the interaction window between 
the lunar tides and the Earth's climate occurs over a 
three month (seasonal) time period centred upon the 
winter solstice (May-Jun-Jul) or the summer solstice 
Hence, the claim by Richard Ray (2007) that:

"Occasional extreme tides caused by unusually 
favorable alignments of the moon and sun are 
unlikely to influence decadal climate, since these 
tides are of short duration and, in fact, are barely 
larger than the typical spring tide near lunar 

is not completely true. 

Indeed if, as is most likely, the interaction between the
lunar tides and Earth's climate primarily takes place
over a monthly to season window then it clear from
the above post that the total tidal potential can vary by
at least +/- 13.5 %  either side of its mean peak value
of 55.5 cm, on a time scale of 8.85 years.


Richard Ray(2007) also claimed that because of the short
duration of each tidal event:

"A more plausible connection between tides and
near-decadal climate is through “harmonic beating”
of nearby tidal spectral lines. The 18.6-yr modulation
of diurnal tides is the most likely to be detectable."

Note: Richard Ray is referring to the beat period 
between the lunar Draconic month and the lunar 
Sidereal month known as the nodal period of lunar 

(27.321661547 x 27.212220817)  = 6793.2277480 days

(27.321661547 - 27.212220817)
                                                      = 18.599 sidereal years

This claim may be partly true.


Ray, R.D., 2007, Decadal Climate Variability: Is 
There a Tidal Connection?, J. Climate20, 3542–3560.

Ray, R.D. and Cartwright, D. E., 2007, Times of peak astronomical
tides, Geophys. J. Int. (2007) 168, 999–1004

Tuesday, December 3, 2013

Scientific Publications and Presentations

UPDATED 04/12/2013

The following is a list of my recent scientific publications
and presentations. I am placing the list on my blog so that
others can have easy access.


Wilson, I.R.G.: The Venus–Earth–Jupiter spin–orbit coupling 
modelPattern Recogn. Phys., 1, 147-158

Wilson, I.R.G., Long-Term Lunar Atmospheric Tides in the 
Southern Hemisphere, The Open Atmospheric Science Journal,
2013, 7, 51-76

Wilson, I.R.G., 2013, Are Global Mean Temperatures 
Significantly Affected by Long-Term Lunar Atmospheric 
Tides? Energy & Environment, Vol 24,
No. 3 & 4, pp. 497 - 508

Wilson, I.R.G., 2013, Personal Submission to the Senate 
Committee on Recent Trends in and Preparedness for 
Extreme Weather Events, Submission No. 106


Wilson, I.R.G.Lunar Tides and the Long-Term Variation 
of the Peak Latitude Anomaly of the Summer Sub-Tropical 
High Pressure Ridge over Eastern Australia
The Open Atmospheric Science Journal, 2012, 6, 49-60

Wilson, I.R.G., Changes in the Earth's Rotation in relation 
to the Barycenter and climatic effect.  Recent Global Changes 
of the Natural Environment. Vol. 3, Factors of Recent 
Global Changes. – M.: Scientific World, 2012. – 78 p. [In Russian].

This paper is the Russian translation of my 2011 paper
Are Changes in the Earth’s Rotation Rate Externally 
Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811.


Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation 
Rate Externally Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811.

Wilson, I.R.G., 2011, Do Periodic peaks in the Planetary Tidal 
Forces Acting Upon the Sun Influence the Sunspot Cycle? 
The General Science Journal, Dec 2011, 3812.

[Note: This paper was actually written by October-November 2007 and submitted to the New Astronomy (peer-reviewed) Journal in early 2008 where it was rejected for publication. It was resubmitted to the (peer-reviewed) PASP Journal in 2009 where it was again rejected. The paper was eventually published in the (non-peer reviewed) General Science Journal in 2010.]


N. Sidorenkov, I.R.G. Wilson and A.I. Kchlystov, 2009, The 
decadal variations in the geophysical processes and the 
asymmetries in the solar motion about the barycentre. 
Geophysical Research Abstracts Vol. 12, EGU2010-9559, 
2010. EGU General Assembly 2010 © Author(s) 2010


Wilson, Ian R.G., 2009, Can We Predict the Next Indian 
Mega-Famine?, Energy and Environment, Vol 20, 
Numbers 1-2, pp. 11-24.

El Ninos and Extreme Proxigean Spring Tides

A lecture by Ian Wilson at the Natural Climate Change
Symposium in Melbourne on June 17th 2009.


Wilson, I.R.G., Carter, B.D., and Waite, I.A., 2008
Does a Spin-Orbit Coupling Between the Sun and the 
Jovian Planets Govern the Solar Cycle?,
Publications of the Astronomical Society of Australia
2008, 25, 85 – 93.

N.S. Sidorenkov, Ian WilsonThe decadal fluctuations 
in the Earth’s rotation and in the climate characteristics
In: Proceedings of the "Journees 2008 Systemes de reference 
spatio-temporels", M. Soffel and N. Capitaine (eds.), 
Lohrmann-Observatorium and Observatoire de Paris. 
2009, pp. 174-177 

Which Came First? - The Chicken or the Egg?

A Presentation to the 2008 Annual General Meeting of the
Lavoisier Society by Ian Wilson


Wilson, I. R. G., 2006, Possible Evidence of the 
De Vries, Gleissberg and Hale Cycles in the Sun’s 
Barycentric Motion, Australian Institute of Physics 17th
National Congress 2006, Brisbane, 3rd -8th December 
2006 (No longer available on the web)